Does the Giza pyramid star-shaft still align with the polar star as it did when built over 4,000 years ago....

When the Giza pyramid was built Thuban (Alpha Draconis) was the pole star, and the shaft still aligns with it, except for a very slight shift attributable to some tectonic shift of the African plate. Stellar proper motion for Thuban is too slight to be noticeable, although were Arcturus the pole star it would be a very large shift.